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What is matrix formulation of geometrical optics ?

Answer:- In general, optical systems are made up of a large number of refracting surfaces (combination of lenses).To obtain the position of the final image due to such a system becomes complicated as the number of elements of an optical system increases.In this section, we develop the matrix method which can be applied with easy under such situations.

Optical path.

Answer:- The optical path length is defined as the product of refractive index and the geometric path length.

Critical angle.

Answer:- Critical angle is the angle of incidence of a ray of light in denser medium such that it's angle of refraction in the rarer medium is 90⁰.

Use of cardinal points.

Answer:- If  cardinal points are known, one can find the image of any object without making a detailed study of the passage of the rays through the system i.e it is not necessary to consider the refraction of the rays at the various surfaces.

Coma or comatic aberration.

Answer:- The effect of rays from an object not situated on the axis of the lens results in an aberration called Coma or comatic aberration.In comatic aberration the image is comet-shaped & hence the name coma.

Chromatic aberration.

Answer:- When a parallel beam of white light is incident on a thin convex lens, then due to prismatic action of lens different colors are focused at different points on the principal axis.This phenomenon is called chromatic aberration.

Distortion.

Answer:- The variation in the magnification produced by a lens for different axial distances results in an aberration called distortion.

Barrel shaped distortion.

Answer:- If magnification produced by lens decreases with increase in distance of object points from axis, then outer parts of image field of view are pulled inward such kind of aberration is called Barrel shaped aberration.

Marginal rays.

Image
Answer:- Rays which are passing through a lens farther away from the axis are refracted more and come to focus closer to the lens are called marginal or peripheral rays.

Pincushion distortion.

Answer:- If magnification produced by lens increases with increase in distance of object points from axis, then outer parts of image field of view are pulled outward such kind of aberration is called pincushion distortion.

Monochromatic aberrations.

Answer:- The defects due to wide-angle incidence and marginal incidence of monochromatic light, are called monochromatic aberrations.It is again divided into five types★Spherical aberration          ★Coma          ★Astigmatism          ★Curvature of field          ★Distortion

First focal point.

Answer:- The first focal point is a point on the principal axis of the lens such that a beam of light passing through it is rendered parallel to the principal axis after refraction through the lens.

Stoke's treatment.

Answer:- This law states that a light wave when gets reflected from a denser medium suffers a phase change of π or path change  λ/2.

Nodal points.

Answer:- Nodal points are points on the principal axis of the optical system where light rays, without refraction, intersect the optic axis.

Refractive index.

Answer:- The refractive index of a medium is defined as the ratio of velocity of light in a vacuum to the velocity of light in the medium.Refractive index defined as above is called as absolute refractive index (n). (I.e n=c/v)

Laws of refraction.

Answer:- ★ FIRST lAW:- The incident ray, the refracted ray & the normal to the interface at the point of incidence all lie in one plane & that plane is perpendicular to the interface separating the two media. ★ SECOND LAW:- The sine of the angle of incidence bears a constant ratio with the sine of the angle of refraction. (I.e sini/sinr = constant)

Laws of reflection.

Answer:- ★ FIRST LAW:- The incident ray, the reflected ray & the normal to the reflecting surface at the point of incidence, all lie in one plane & that plane is perpendicular to the reflecting surface. ★ SECOND LAW:- The angle of incidence is equal to the angle of reflection(i.e i=r).

Principle of Reversibility.

Answer:- It states that if a ray of light, after suffering a number of reflections and/or refractions has its path reversed, at any stage, it will retrace itself back to the source along the same path.

Dispersion.

Answer:- When white light passes from one optical medium to another, different colors of the light split, and this phenomenon of splitting of light into its components as a result of refraction is called dispersion.

Matrix formulation of geometrical optics.

Answer:- In general, optical systems are made up of a large number of refracting surfaces (combination of lenses).To obtain the position of the final image due to such a system becomes complicated as the number of elements of an optical system increases.under such situations matrix method is used.